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434

Rolled Beam.

,1!

Momental Strength of Wrought Iron Rolled Beam

(the section being given at Fig. 388).—Referring every fibre to
c B or D E we obtain the shaded stress areas. As these change
in contour very abruptly, it is best to divide into 20 parts to
find the mean width '6895, Then "6895" x 275"= r8$6 area in
sq. ins. The arm may be found by calculation or by hanging up
the paper area from two positions, the first method being shewn
in the diagram, and the result found as 2*33" on either side,
Then Z = area x arm, and

Moment of resistance =/x 1*896 X4*66   =/8'&35
= 4 x 8-835 = 35-34ton inches

In such beams/t= 5 tons and_/c = 4 tons, so the lowest value
has been taken. By the approximate formula,

Moment —Jcach =4x1 '625 x 5 = 32'5 ton inches.

Momental Strength of Steel Rail (Fig. 389).—By
cutting out the section and hanging it, the neutral axis is found
at 1-56" from bottom and 1-69 from top; the limiting- line is
therefore BC. A second limiting line is drawn at DE, also 1*69
from axis, every fibre now referred to B c or D E, and the
stress areas obtained. Cutting these out, their centres can be
found, giving the arm 2*5", and their areas by dividing each
into 10 parts vertically. Then (mean-width x height) gives
, 751" * r69"= 1*27 for top area, and '867"x 1-56" = 1*35 for
bottom, area. It is very difficult to get them exactly equal
graphically, so the average 1*31 sq. ins. must be taken. Then
Moment of resistance =/x area x arm

= 6 x i '31 x 2 *5 = 19*65 ton inches.

Mornental Strength of Cast Iran Beam (Fig. 390).
—c D A B is the beam section, whose axis is found at E, Draw
perpendiculars F G and M NT. Set off H G = i J and M K = 4,
representing/i andj£ respectively, and draw Hjand KL through
axis, giving F j as 2§ and L N as 2^. This shews that if/c be the
limiting stress the tension flange would be stressed to z\ tons,
or dangerously; while/t at i£ tons would only'stress the com-
pression flange at 2§ tons, or safely, ft is therefore the limiting
stress, and A B the limiting line below E, while a corresponding